Exploring the role of cyclodextrins as a cholesterol scavenger: a molecular dynamics investigation of conformational changes and thermodynamics

This study presents a comprehensive analysis of the cholesterol binding mechanism and conformational changes in cyclodextrin (CD) carriers, namely βCD, 2HPβCD, and MβCD. The results revealed that the binding of cholesterol to CDs was spontaneous and thermodynamically favorable, with van der Waals interactions playing a dominant role, while Coulombic interactions have a negligible contribution. The solubility of cholesterol/βCD and cholesterol/MβCD complexes was lower compared to cholesterol/2HPβCD complex due to stronger vdW and Coulombic repulsion between water and CDs. Hydrogen bonding was found to have a minor role in the binding process. The investigation of mechanisms and kinetics of binding demonstrated that cholesterol permeates into the CD cavities completely. Replicas consideration indicated that while the binding to 2HPβCD occurred perpendicularly and solely through positioning cholesterol's oxygen toward the primary hydroxyl rim (PHR), the mechanism of cholesterol binding to βCD and MβCD could take place with the orientation of oxygen towards both rims. Functionalization resulted in decreased cavity polarity, increased constriction tendency, and altered solubility and configuration of the carrier. Upon cholesterol binding, the CDs expanded, increasing the cavity volume in cholesterol-containing systems. The effects of cholesterol on the relative shape anisotropy (κ2) and asphericity parameter (b) in cyclodextrins were investigated. βCD exhibited a spherical structure regardless of cholesterol presence, while 2HPβCD and MβCD displayed more pronounced non-sphericity in the absence of cholesterol. Loading cholesterol transformed 2HPβCD and MβCD into more spherical shapes, with increased probabilities of higher κ2. MβCD showed a higher maximum peak of κ2 compared to 2HPβCD after cholesterol loading, while 2HPβCD maintained a significant maximum peak at 0.2 for b.


Details of Free energy computations
Here, two sets of energy calculations were performed.

ΔG1: Decoupling of Cholesterol interactions in Water:
The final configuration obtained from a 200 ns simulation of a system comprising water and cholesterol was used as the initial configuration for calculating the solvation free energy.The decoupling of cholesterol from the surrounding environment (solely water) was achieved through 25 λ values ranging from 0 to 1.After the simulation, a value of 11.18 kJ/mol was obtained for the solvation free energy of cholesterol.ΔG2: Decoupling of Cholesterol interactions in the presence of Water/Cyclodextrins: In this study, the initial configurations for calculating free energy were obtained from the final configurations of 200 ns simulations for each water/cholesterol/cyclodextrin system.Cholesterol was fully loaded into the cyclodextrin cavities during these simulations.The decoupling of cholesterol from the environment (water/cyclodextrins) was achieved using 25 λ values ranging from 0 to 1.The resulting free energy values for βCD, MβCD, and 2HPβCD were -66.31, -64.37, and -57.76 kJ/mol, respectively.Following the thermodynamic cycle detailed by Mobley et al. (reference 40), the binding free energy of cholesterol to cyclodextrins was determined as follows: In the above schematic, ΔG1 is ΔGsolvation of Cholesterol in water and ΔG2 is ΔGcomplexation of CD/Cholesterol, and ΔGtransfer = 0. Considering the following equations, the binding free energy could be calculated:

ΔGbind = ΔGcomplexation + ΔGdesolvation ΔGsolvation = -ΔGdesolvation ΔGbind = ΔGcomplexation -ΔGsolvation
In both the complex (ΔG2) and solvent (ΔG1) phases of the thermodynamic cycle, the Coulombic interactions of cholesterol were completely annihilated before decoupling the vdW interactions.This annihilation of Coulombic interactions was performed during the first twelve λ.Subsequently, in the next thirteen λ, the vdW interactions were decoupled.

Calculation methods for area and volume of cavity
The area of CDs cavity was calculated by the following equation: Where   is the distance between each hydroxyl group and the center of O1 atoms, and the hydroxyl groups at 6-and 3-positions are used for representing the cavity area of primary and secondary hydroxyl rims, respectively.
The CD cavity has a shape that resembles a conical hourglass.As a result, we can approximate its volume by combining the volumes of the truncated cones located at the top and bottom of the cavity, as shown below.
One can determine the volume of a truncated cone with a small radius "r", a large radius "R", and a height "h" by considering its geometry as follows: The radius of the O1 rim (Figure 1) was used as the small radius of the cones, while the radius of O2 rim and O6 rim was used as the large radius of the top and the bottom cone, respectively.The height, h, of the cones is sum of h12 and h16 listed in Table 1.Table S7: Analyzing of energies in different simulated systems that containing βCD a .a All results were obtained from the last 10 % of the simulation time.
Table S8: Analyzing of energies in different simulated systems that containing MβCD a .a All results were obtained from the last 10 % of the simulation time.
Table S9: Analyzing of energies in different simulated systems that containing 2HPβCD a .a All results were obtained from the last 10 % of the simulation time.

Figure S1 :
Figure S1: Molecular structure and the numbering in Cholesterol (a), and main skeleton of βCD derivatives (b)

Figure S7 :
Figure S7: Radial distribution function (RDF) of water around CDs in different simulated systems.

Figure S8 :
Figure S8: The relative shape anisotropy parameter (a), and the Asphericity parameter (b) of βCD in different simulated systems.

Figure S9 :
Figure S9: The relative shape anisotropy parameter (a), and the Asphericity parameter (b) of MβCD in different simulated systems.

Figure S10 :
Figure S10: The relative shape anisotropy parameter (a), and the Asphericity parameter (b) of 2HPβCD in different simulated systems.

Figure S11 :
Figure S11: The total interaction energy between water/CDs in different simulated systems.

Table S7 -
S9: Analyzing of energies in different simulated systems that containing βCD, MβCD,

Table S1 :
Number of water molecules in different spheres inside the βCD cavity a .
a All results were obtained from the last 10 % of the simulation time.

Table S2 :
Number of water molecules in different spheres inside the MβCD cavity a .
a All results were obtained from the last 10 % of the simulation time.

Table S3 :
Number of water molecules in different spheres inside the 2HPβCD cavity a .

Table S4 :
Conformational Parameters Describing Molecular Arrangement of βCD in different simulated systems a .
a All results were obtained from the last 10 % of the simulation time.

Table S5 :
Conformational Parameters Describing Molecular Arrangement of MβCD in different simulated systems a .
a All results were obtained from the last 10 % of the simulation time.

Table S6 :
Conformational Parameters Describing Molecular Arrangement of 2HPβCD in different simulated systems a .
a All results were obtained from the last 10 % of the simulation time.

Table S10 :
Average number of different hydrogen bonds in the βCD simulated systems a .All results were obtained from the last 10 % of the simulation time. a

Table S11 :
Average number of different hydrogen bonds in the MβCD simulated systems a .
a All results were obtained from the last 10 % of the simulation time.

Table 12 :
Average number of different hydrogen bonds in the 2HPβCD simulated systems a .
a All results were obtained from the last 10 % of the simulation time.

Table S13 :
The number of acceptors and donors involved in hydrogen bonding in this study.